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Question 2 [10 marks] Automated teller machines (ATMs) have made it easier and faster for customers...

Question 2 [10 marks] Automated teller machines (ATMs) have made it easier and faster for customers to check their account balances, transfer money, and obtain cash. Many banks are now considering the next generation of ATMs, which will feature news headlines, full-motion video, and tickets to events. In a random sample of 500 customers, 280 said ATMs should offer postage stamps.

a. [2 marks] Find the sample proportion of customers who believe ATMs should offer postage stamps, and check the non-skewness criterion. Show all your work in order to get full marks.

b. [4 marks] Find a 99% confidence interval for the true proportion of customers who believe ATMs should offer postage stamps. Show all your work in order to get full marks.

c. [4 marks] A bank official claims that the proportion of customers who believe ATMs should offer postage stamps is 0.60. Is there any evidence to refute this claim? Show all your work in order to get full marks.

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